Group identities on units of group algebras
Let \(U\) be the group of units of the group algebra \(FG\), where \(G\) is a group and \(F\) is a field. This paper is concerned with determining when \(U\) satisfies a group identity. If \(G\) is torsion, then this question was settled in recent years, thereby yielding an affirmative solution to Hartley's problem. Here, the authors deal with groups that are nilpotent modulo torsion elements and they offer a full characterization when \(F\) is infinite. In particular, if \(p\geq 0\) is the characteristic of the field, then they show that the set of all \(p\)-elements \(P\) must necessarily form a normal subgroup of \(G\), and that the nature of the answer splits into two cases according to whether \(P\) has bounded exponent or not.
scientific article; zbMATH DE number 1441820
scientific article